PHYSICAL REVIE% B VOLUME 50, NUMBER 24 Transferable tight-binding model for Si-H systems 15 DECEMBER 1994-II Qiming Li and R. Biswas Microelectronics Research Center and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (Received 17 June 1994) We develop a tight-binding molecular-dynamics model for Si-H systems that incorporates relevant physics of charge-transfer and local-environment dependence of atomic interactions. Our model was fitted to silane, and yields electronic levels of disilane in good agreement with experiment and vibrational frequencies that are consistent with the experimental trend for SiH„groups. The model describes well the formation energies and energy surfaces for the different charge states of H in c-Si, including the stability of the bond-centered site for positive and neutral charge states and the stability of the tetrahedral site for negative charge states. The model also describes well the structural and electronic properties of a-Si:H models. The present approach utilizes quantum- mechanical forces, incorporates important electronic effects, and is suitable for studying complex phenomena such as H diffusion and dynamics of c-Si or a-Si:H. I. INTRODUCTION It is well recognized that the presence of hydrogen strongly affects the electronic and optical properties of semiconductor microelectronic materials. In crystalline silicon, hydrogen is a common impurity that is known to passivate the electrical activity of shallow dopants. On the other hand, in amorphous silicon a significant amount of H is necessary to passivate defects and pro- duce electronic quality material with a high photocon- ductivity and low density of gap states. Porous silicon is another recent application where a large amount of H is also present and needed to increase luminescence efKiciencies. 2 Many of these interesting phenomena, how- ever, are not well understood. The behavior of hydrogen in crystalline semiconduc- tors has recently been understood by the pioneering calculations of Van de Walle et at. 3 who, using first- principles calculations, predicted that the stable position of H in c-Si depended on the charge state, with the tetra- hedral (T) site being most stable for the negative charge state (n-type Si) and the bond-centered (BC) site being the stable state for the neutral and positive charge states (p-type Si). These and other similar calculations in- corporating H-dopant complexes have described well the passivation of dopants in Si by H and support the large body of experimental evidence in these systems. While such first-principles calculations have been very successful for predicting the properties of H in crystalline systems, there are a large variety of complex systems such as amorphous hydrogenated silicon (a-Si:H) or porous silicon where first-principles calculations are exceedingly difficult and virtually not feasible for large systems (i.e. , hundreds of atoms). Problems in these complex sys- tems include long-range H diffusion, the nature of light- induced defects in a-Si:H, the growth of realistic a- Si:H films, and the origin of the band gap in porous sili- con. For such complex systems it is necessary to develop more robust methods that are computationally less inten- sive but contain the essential physics such that reliable information can be obtained. Classical molecular dynamics (MD) with either two- and three-body potentials ' or many-body potentials have been developed for Si-H systems, ' and used for computationally intensive molecular-dynamics sim- ulations. However classical molecular dynamics cannot address purely quant»m-mechanical phenomena involv- ing electronic states, such as Jahn-Teller distortion or defect states in semiconductors. A very promising sim- ulation approach is the tight-binding (TB) methodis is which is intermediate between first-principles i and classical molecular-dynamics methods in the level of so- phistication, and which contains the important aspects of the electronic properties. Tight-binding molecular dynamics (TBMD) has emerged as a very robust method for simulating prop- erties of pure C as well as Si systems. Recent successes include modeling properties of fullerenes and develop- ment of models for Si (Ref. 23) which have shown promise in modeling the bulk phases and melting of silicon. These TB models for Si were based on the minimal sp orbital basis set to model the electronic properties, and utilize quantum-mechanical forces in the molecular-dynamics simulation. Previous TB approaches for Si-H systems by Allen and Mele and subsequently an improved TB model of hy- drogen silicon interaction by Min et al. , both utilizing an s-orbital for H, were successful in describing silane and the lattice dynamics and structural properties of an H- covered Si(111) surface. We would expect a Si-H model to not only describe well the strong Si-H bonds but to also quantitatively describe the energy of weakly bonded H in e-Si, if it is to be reliable in simulating more complex systems such as a-Si:H. However, the simple extensions of previous TB models do not account for several im- portant features of H in c-Si, especially the formation energies and energy surfaces for difFerent charge states of H in c-Sl. 0163-1829/94/50(24)/18090(8)/$06. 00 50 1994 The American Physical Society